Transcript 8-5 Angles of Elevation & Depression

8-5 Angles of
Elevation & Depression
Angles of Elevation

Angle of Elevation: The angle
between the line of sight and the
horizontal when an observer looks
upward.
Angle of Elevation
Example 1

Find the angle of elevation of the Sun
when a 7.6 meters flagpole casts a 18.2
meter shadow. Round to the nearest
tenth of a degree.
Tan = Opposite/Adjacent
Tan x = 7.6/18.2
x = tan-1 (7.6/18.2)
x = 22.7°
7.6 m
18.2 m
Angle of Depression

Angle of Depression: The angle between
the line of sight when an observer looks
downward and the horizontal.
Angle of Depression
Example 2

A wheelchair ramp is 3 meters long and
inclines at 6°. Find the height of the ramp
to the nearest tenth of a centimeter.
Sin = Opposite/Hypotenuse
3m
Sin 6° = x/3
6°
?
3(Sin 6°) = x
31.4 cm = x
Example 3

Two boats are observed by a parasailer 75
meters above a lake. The angles of
depression are 12.5° and 7°. How far
apart are the boats?
Tan 7° = 75/x1
x1 (Tan 7°) = 75
7°
x1 = 75/Tan 7°
x1 ≈ 610.8
75 m
12.5°
Tan 12.5° = 75/x2
x2 (Tan 12.5°) = 75
x2 = 75/Tan 12.5°
x2 ≈ 338.3
12.5°
Answer = x1 – x2 = about 273 m
7°
Try these
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p. 466 #1
Answer: about 2.2°
#2
Answer: about 169.9 m
#3
Answer: C…x = 150/tan12°
Homework #53 p. 467 4-18 even,
19-21, 27-28